Time Series Analysis – Question Bank www.ift.world LO.a: calculate and evaluate the predicted trend value for a time series, modeled as either a linear trend or a log-linear trend, given the estimated trend coefficients For a log linear trend model, the slope coefficient is and the intercept coefficient is 10 The predicted trend value at time t = 20 is closest to: A 110 B 5.92 C 62.34 LO.b: describe factors that determine whether a linear or a log-linear trend should be used with a particular time series and evaluate limitations of trend models In which of the following scenarios will a log-linear trend model be most likely used? A When the variable grows at a constant rate B When the variable increases over time by a constant amount C The Durbin Watson statistic is significantly different from 2.0 LO.c: Explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary Which of the following is least likely a requirement for a time series to be covariance stationary? A The expected value of the time series changes at a constant rate over time B The time series’ volatility around its mean does not change over time C The covariance of the time series with leading or lagged values of itself is constant LO.d: Describe the structure of an autoregressive (AR) model of order p and calculate oneand two-period-ahead forecasts given the estimated coefficients Consider an AR(1) model with the following equation value of x is 4, the two-period-ahead forecast is closest to: A 2.5 B 3.3 C 3.16 If the current LO.e: Explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series The correlations of the error terms from the estimation of an AR(1) model using a sample with 144 observations is presented in the following figure Based on this information which of the following statements is most appropriate? (The critical two tail t-value at the 5% significance level and 142 degrees of freedom is 1.98) Lag Autocorrelation 0.124 0.148 0.166 Copyright © IFT All rights reserved Page Time Series Analysis – Question Bank www.ift.world A The AR model is correctly specified B The AR model is not specified correctly because the autocorrelations of the residuals for lag are statistically different from C The AR model is not specified correctly because the autocorrelations of the residuals for lag are statistically different from LO.f: Explain mean reversion and calculate a mean-reverting level For a regression model A 12.5 B 3.125 C 4.65 , the mean reverting level is closest to: LO.g: Contrast in-sample and out-of-sample forecasts and compare the forecasting accuracy of different time-series models based on the root mean squared error criterion Which of the following statements is most accurate? When comparing two autoregressive models: A the model with the higher root mean squared error (RMSE) for out-of-sample data is expected to produce better predictive power in the future B the model with the lower root mean squared error (RMSE) for in-sample data is expected to produce better predictive power in the future C the model with the lower root mean squared error (RMSE) for out-of-sample data is expected to produce the better predictive power in the future LO.h: Explain the instability of coefficients of time-series models Analyst 1: The coefficients of models estimated with shorter time series are usually less stable than those with longer time series Analyst 2: If there has been a dramatic change in the underlying economic environment, then historical data may not provide a reliable model A Analyst is correct B Analyst is correct C Both analysts are correct LO.i: Describe characteristics of random walk processes and contrast them to covariance stationary processes A time series that follows a random walk process, has the following expression Which of the following statements is least accurate? A The expected value of the error term E( ) is for a random walk with or without drift B for a random walk without drift and for a random walk with drift C for a random walk without drift and for a random walk with drift Copyright © IFT All rights reserved Page Time Series Analysis – Question Bank www.ift.world LO.j: Describe implications of unit roots for time-series analysis, explain when unit roots are likely to occur and how to test for them, and demonstrate how a time series with a unit root can be transformed so it can be analyzed with an AR model 10 An analyst is checking for unit root problem and has performed the Dickey Fuller test He found that the null (g=0) cannot be rejected Which of the following statements is most accurate? A The time series does not have a unit root problem B The time series is covariance stationary C The time series has a unit root problem LO.k: Describe the steps of the unit root test for nonstationarity and explain the relation of the test to autoregressive time-series models 11 If a time-series model has a unit root problem then which of the following transformations can most likely be performed to solve this problem? A Log-linear transformation B First-differencing C Dickey Fuller transformation LO.l: Explain how to test and correct for seasonality in a time-series model and calculate and interpret a forecasted value using an AR model with a seasonal lag 12 The following table shows the autoregression output for Log-quarterly sales of a retailer using an AR(1 model) The number of observations are 40.Which of the following statements is most accurate? (At a significance level of 5% and 37 degrees of freedom the critical t-value is 2.026) Residual Lag t-statistic -0.45 -0.02 0.015 4.815 A Seasonality is present in the time series B Seasonality is not present in the time series C The AR model is specified correctly LO.m: Explain autoregressive conditional heteroskedasticity (ARCH) and describe how ARCH models can be applied to predict the variance of a time series 13 The regression results for a ARCH(1) model are shown below If the current period squared error is 0.4356, the variance of the error terms in the next period is closest to: Coefficients p-value Constant 5.6521